Global extreme values

determine the global extreme values of the function on the given domain:

f(x,y)=x^2+2y^2 , 0<=x,y<=1

3. The attempt at a solution

- I know you need to evaluate the critical points first and then use the boundary to find the maximum and minimum values, but I can't seem to get the right answer. I think I'm just misunderstanding the way you go about a problem like this. Please help.

Finding critical points is one way to solve it, but it's a little tedious and unnecessary. Just start by examining the function [tex]f(x,y) = x^2 + 2y^2 [/tex].

Note that the function is greater or equal to 0. That should tell you something about the extreme values. And note that while x is bounded below, it's not bounded above, what does that say about the function?

Finding critical points is one way to solve it, but it's a little tedious and unnecessary. Just start by examining the function [tex]f(x,y) = x^2 + 2y^2 [/tex].

Note that the function is greater or equal to 0. That should tell you something about the extreme values. And note that while x is bounded below, it's not bounded above, what does that say about the function?

- would the function always being great than or equal to zero mean that the global minimum would be 0?

with x not being bounded above, that would mean that it contains points arbitrarily far from the origin, but I'm not sure what that would mean for finding the maximum.

If the function has a max, it must be on the boundary of 0<=x,y<=1, yes?

- right. so how would you set up the problem to find that max? the problem before it, I wasn't sure if I did it right, but I got the right answer. I did this problem the same way and got the wrong answer, so I just think I got lucky doing the problem before incorrectly. So I guess I'm not really sure how to set a problem like this up.

- right. so how would you set up the problem to find that max? the problem before it, I wasn't sure if I did it right, but I got the right answer. I did this problem the same way and got the wrong answer, so I just think I got lucky doing the problem before incorrectly. So I guess I'm not really sure how to set a problem like this up.

The boundary consists of four line segments. One of them is x=0, 0<=y<=1. What's the maximum along that segment? What about the other three?